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Use the relation of dominance to solve the rectangular game whose payoff matrix to A is given in the following table.

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First checking for saddle point:

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Maximin value = 2; minimax value = 4

Hence there is no saddle point.

By rules of dominance:

  • Row I is dominated by row III. So the matrix reduces to:

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  • Column I is dominated by column III:

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  • Column II is dominated by the average of columns III & IV:

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  • Row II is dominated by the average of row III & IV:

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Finding probabilities by method of oddments:

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$\text{Value of the game} = 4 × \dfrac23 + 0 × \dfrac13 = \dfrac83$

OR $= 0 × \dfrac23 + 8 × \dfrac13 = \dfrac83$

$\text{Optimal strategy for A} = \bigg(0, 0, \dfrac23 , \dfrac13 \bigg) \\ \text{Optimal strategy for B} = \bigg(0, 0, \dfrac23 , \dfrac13 \bigg) \\ \text{Value of the game} = \dfrac83$

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